An Act to facilitate compliance by Australia with obligations under the Rome Statute of the International Criminal Court, and for related purposes
Part 4 Other requests by ICC
Division 3—Restrictions on provision of assistance
56 Competing requests
(1) If a request for cooperation is made and a foreign country makes a request for assistance to which Australia is under an international obligation to respond, the Attorney-General must, after consultation with the ICC and that country, try to comply with both requests.
(2) For the purposes of subsection (1), the Attorney-General may do either or both of the following:
postpone the execution of either of the requests;
attach conditions to the provision of assistance under either or both of the requests.
(3) If it is not possible to resolve the issue by consultation, the method of dealing with the requests must be resolved in accordance with sections 57 to 61.
Competing request
Admissibility challenge - competing request - consultations with the Court
Competing request - same conduct - State not Party
Competing request - same conduct - State not Party - international obligation
Competing request - different conduct - international obligation to extradite
EDIT.